Prediction of Far-Field Pattern Characteristics ofPhased Array Fed Reflector Antennas By Modeling

Only a Small Part of the Array – Case Study ofSpaceborne Radiometer Antennas

O. A. Iupikov∗, A. A. Roev∗, M. V. Ivashina∗∗Chalmers University of Technology, Goteborg, Sweden, oleg.iupikov@chalmers.se, roev@chalmers.se,

marianna.ivashina@chalmers.se

Abstract—In this work we present an approach of simplifiedanalysis of focal plane array (FPA) systems, in which phased-shifted versions of the simulated embedded element pattern(EEP) of the center element are used to compose a set of all EEPsof the full-scale array and thereafter combined with the optimumweighting coefficients in order to find the total pattern of the feed.Although, the EEPs of dense array antennas are generally notidentical (due to the array antenna mutual coupling and edgetruncation effects), for typical FPA excitation scenarios, wherethe array edge elements have relatively low weights to producethe desired illumination of the reflector, this simplified approachhas been found sufficiently accurate.

Index Terms—reflector antenna feeds, array antennas, mi-crowave radiometers

I. INTRODUCTION

Recent advances in radio-frequency and digital electronicshave allowed for the design of novel antenna systems, whichhave superior beamforming capabilities. Examples of suchsystems are spaceborne antennas for ocean surveillance andsatelitte communication; they are required to provide multiplehigh-efficiency beams (with extremely low side-lobes or cross-polarization) and operate at several frequency bands (typicallyL-, C-, X and Ku-bands), while having a compact single-antenna design. These challenging requirements can be metby using dense focal plane arrays (FPAs) feeding a reflector(or a lens), or directly-radiating sparse irregular arrays [1],[2]. However, there are common problems with such largeand multi-scale antenna designs, including fast and accurateelectromagnetic analysis as well as cost-efficient prototypedevelopment. Different approaches have been proposed toovercome these problems for the sparse arrays, where per-formance of the whole antenna system is evaluated throughthe analysis of a small part of it (e.g. [1], [2]).

In this work we address this problem for the case ofFPA systems, and in particular present a validated simplifiedapproach where a reduced-size FPA simulations are usedto predict the performance of the whole array feeding thereflector antenna.

II. ANTENNA GEOMETRY AND SPECIFICATIONS

To demonstrate the proposed approach we have considereda conical-scan offset parabolic reflector antenna (projectedaperture diameter is 5 m, focal length is 3 m and clearance is1 m) with the 67-element array feed. This antenna system iscurrently being considered for potential future ocean missionsby ESA [3]. The requirements for this mission are givenin Table I, [4], in terms of standard performance metricsfor oceanographic surveys. For the given satellite altitudeand incidence angle, the radiometric requirements can betransfered [5] to the antenna system specifications as shownin Table II.

TABLE IRADIOMETRIC REQUIREMENTS FOR FUTURE OCEAN MISSIONS

Freq.,[GHz]

Bandwidth,[MHz]

Polari-zation

Radiometricresolution,

[K]

Bias,[K]

Spatialresolution,

[km]

Dist.tocoast,[km]

L-band:1.404−1.423

19 V, H 0.15 0.25 100 50-100

C-band:6.8−7.07.2−7.4

200 V, H 0.30 0.25 20 15-20

TABLE IIANTENNA REQUIREMENTS

Antenna characteristic L-band C-bandNumber of beams 4 2Cross-polar. power over the Earth < 0.34 %Power over the land < 0.28 %Projected aperture diameter of the reflector 5 m

In previous system-level studies, we have applied this sim-plified approach to cross-compare different radiometer systemconcepts, i.e. a traditional conical-scan off-set parabolic reflec-tor antenna vs. a wide-scan torus reflector system [6], [7], aswell as to perform parametric studies for the FPAs to define theoptimal number of antenna elements, inter element spacing,and the arrangement of FPAs operating at different bands [6],[8], [9]. In the current work, we validate this approach for the

case of a wideband Vivaldi antenna element FPA feeding theconical-scan reflector antenna, and use for this purpose therequirements in Table I. To simplify the prototyping phase,our focus will be on the high frequency performance only (C-band), for which the small-size array demonstrator has only24 elements, while the operational bandwidth of the designedfull-scale array covers both L- and C-bands.

III. ARRAY ANTENNA DESIGN

The Vivaldi antenna element in [10], which most closelymeets the wide-band requirements of the project, was chosenas a reference: it has the relative bandwidth greater than 6:1over wide scan range (±45 deg). Since the geometry of thereferred TSA in [10] is for the frequency band of 0.4–1.6 GHz,we have scaled up this design with some modifications relatedto the following practical implementation aspects:

• to improve the mechanical stability;• to improve the matching for the reference impedance

of 50 Ohm (in opposite to the original design, where70 Ohm LNAs are used).

Thus a new element geometry of a dual-polarized phasedarray has been optimized and analyzed with the aid of periodicboundary conditions. The slotline width, rate of exponentialslotline, cavity length, stub radius and stripline width werechosen as variable parameters. The main goal was to achievethe impedance matching condition with magnitude of theactive reflection coefficient less than −10 dB within ±45 degscan range. The optimization have been performed with thecommercially available EM software HFSS and CST.

The final antenna and feed geometries with dimensions areshown in Fig. 1(a) and 1(b), respectively. Tapered slot profileis determined by curve:

y = C1eRx + C2, (1)

where R is the rate of exponential slotline, and coefficientsC1 and C2 are defined as

C1 =y2 − y1

eRx2 − eRx1(2)

C2 =y1e

Rx2 − y2eRx1

eRx2 − eRx1, (3)

where points (x1, y1) and (x2, y2) determine a slot width inthe excitation region and the aperture, respectively.

(a) (b)

x1 y1 x2 y2 R

13.21 0.25 82.57 13.92 0.04

Fig. 1. Geometrical dimensions of (a) the proposed TSA element and (b)feeding plate. All dimensions are given in [mm].

Based on the simulations, a prototype of the small-scaledual-polarized array, comprising 24 elements, was designedand manufactured (Fig. 2). The array antenna structure consistsof 4 orthogonally placed brass sheets with 3 TSA elements perpolarization. All elements are mounted on the 250x250 mmaluminum ground plane. Each element is excited directly by aPCB feed with the SMA connector located under the groundplane.

Fig. 2. Photo of the manufactured reduced prototype.

IV. ANALYSIS METHODOLOGY AND NUMERICAL RESULTS

For typical FPA excitation scenarios, the antenna elementsat the edge of the array have significantly (-5...-15 dB) lowerweighting coefficients relatively to the elements in the center.This implies that the differences in the embedded elementpattern shapes, introduced by the edge effects, will haverelatively weak contribution to the total compound beam ofthe array when all elements are excited. This motivates ourassumption on the identical EEPs that can be taken to be thesame as the pattern of an element in the center. Such approachcan greatly speed up the numerical analysis of a reflectorantenna system, which is very important for optimization.

The antenna specifications (see Table II) define the requiredarray layout and aperture area, which are shown in Fig. 3(a). Inorder to validate the proposed analysis approach, we have usedthe full-wave simulation results for this array as the referencefor the following simplified models:

1) Simplified model I, where FPA EEPs are phase-shiftedversions of the EEP of the central element (elementNo.18), which was obtained for the full-scale array;

2) Simplified model II, where FPA EEPs are phase-shiftedversions of the EEP of the central element (elementNo.5), which was obtained for the small-sized array,shown in Fig. 3(b).

Figure 4 shows the EEPs for all these cases.Figure 3(c) shows the weighting coefficients for Simplified

models I and II have been found through the dedicatedoptimum beamforming procedure detailed in [11] that aimsto satisfy the radiometric requirements. The coefficients forthe small-sized array have been chosen to be a sub-set of thecalculated coefficients that correspond to the most stronglyexcited elements; they are shown in Fig. 3(d).

−40 −30 −20 −10 0

1 2 3 4 5 6 7

8 9 10 11 12 13 14

15 16 17 18 19 20 21

22 23 24 25 26 27 28

29 30 31 32 33 34 35

36

37

38

39

40

41

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45

46

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48

49

50

51

52

53

54

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56

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67

(a)

1 2 3

4 5 6

7 8 9

10 11 12

13

14

15

16

17

18

19

20

21

22

23

24

(b)

-31.1 -27.3 -30.2 -33.6 -36.5 -36.6

-30.8 -10.0 -4.6 -9.3 -21.9 -34.5

-28.8 -5.2 0.0 -4.3 -18.4 -27.5 -31.5

-30.4 -10.1 -4.7 -9.4 -22.0 -33.8

-31.5 -27.3 -30.2 -33.5 -36.9 -37.4

−40

−30

−20

−10

0

(c)

-10.0 -4.6 -9.3

-5.2 0.0 -4.3

-10.1 -4.7 -9.4

-27.3 -30.2 -33.5

−40

−30

−20

−10

0

(d)

Fig. 3. (a,c) Full-size array and (b,d) small-sized array layouts, and thecorresponding weighting coefficients of the horizontally-polarized elementsat 6.9 GHz (weighting coefficients of the orthogonally-polarized elements arenot shown due to their low values), in [dB]

−90 −75 −60 −45 −30 −15 0 15 30 45 60 75 90−20

−15

−10

−5

0

5

10

θ, deg

|Gco|,|G

xp|,

[dB

i]

Subtended angleCo-polar, E-planeCo-polar, H-planeXp-polar, D-plane

Fig. 4. (solid lines) The E-, H- and D-plane embedded element pattern (EEP)cuts of the 67-element array at C-band, simulated with the finite elementmethod in HFSS software (reference case), where the bold lines denote theEEP of the central element (no. 18) of the full-size array, used for Simplifiedmodel I; and the dashed lines denote the EEP of the central element (no. 5)in the small-sized array, used for Simplified model II.

To cross-compare the array performances, we have used theactive reflection coefficient [12] of the central element, whenall antenna elements are excited with a certain complex-valuedweight, as well as the radiometric characteristics specified inTable III.

The full-sized and small-scaled arrays have been modeledusing a fullwave approach and the active reflection coefficientof the most excited elements are shown in Fig. 5. The redcurve (a) corresponds to the fully-excited full-sized array;dashed curve (b) is for the same array when only 24 elements(highlighted in Fig. 3(a)) are active; and the blue curve (c)corresponds to the most excited element of the small array,when the same weight coefficients are used as for the previouscase.

6.7 6.8 6.9 7 7.1 7.2 7.3 7.4 7.5−30

−20

−10

0

Frequency, [GHz]

|Γac

t|,[d

B]

(a) 67-elem array, all active(b) 67-elem array, 24 active(c) 24-elem array, all active

Fig. 5. Central active reflection coefficient for (a) full-size array, when allelements are excited to form the optimum beam; (b) full-size array, whenonly 24 most strongly excited elements are used in the calcultion; and (c)24-element array with the same weight coefficients as for the previous case.The operating frequency bands are shown as green strips.

−60 −40 −20 0 20 40 60−40−35−30−25−20−15−10−50

θ, [deg]

|Gco|,|G

xp|,[dB]

Subtended angleReference modelSimplified model ISimplified model II

Fig. 6. Comparison of the total primary patterns obtained for the referencefull-wave array model and Simplified models I and II. Solid and dashed linesshow the co-polarized (at φ = 0◦) and cross-polarized (at φ = 45◦) fieldcomponents, respectively.

−3 −2.5 −2 −1.5 −1 −0.5 0 0.5 1 1.5 2 2.5 3−60

−50

−40

−30

−20

−10

0

θ, [deg]

|Gco|,|G

xp|,[dB]

Reference modelSimplified model ISimplified model II

Fig. 7. Comparison of the total secondary patterns obtained for the referencefull-wave array model and Simplified models I and II. Solid and dashed linesshow the co-polarized (at φ = 0◦) and cross-polarized (at φ = 45◦) fieldcomponents, respectively.

As one can see, the curves (a) and (b) are nearly identical.This is expected, since they are for the same EM model of thefull-sized array, and the array elements outside the highlightedarea are weakly excited, so they have neglifible effect onthe central element active reflection coefficient. The result (c)differs from (b) since the edge truncation effects are strongerin the smaller array. Nevertheless, the overall prediction of thereference reflection coefficient (a) is good enough for such a

TABLE IIIFINAL RADIOMETER CHARACTERISTICS AT C-BAND (6.9 GHZ)

Radiometer characteristic Requirement Reference model Simplified model I Simplified model IIBeam efficiency [%] 96.6 97.8 96.5Cross-polar. power, [%] < 0.34 0.19 0.34 0.71Distance to coast, [km] ≤ 15 11.4 14.5 13.6Beam width, [deg] 0.648 0.664 0.647Average footprint, [km] 20 18.8 19.5 18.6Footprint ellipticity 1.69 1.91 1.60

strongly-coupled antenna array.The total primary- and secondary patterns of the array, i.e.

the pattern before and after reflection from the dish) are closs-compared for the above cases in Fig. 6 and Fig. 7, respectively.

One can see the overall shape of the co-polar pattern of thereference full-wave array model has been predicted rather wellwith both simplified models, however the cross-polar com-ponents obtained with the latter appear to be higher. Similarobservations can be made for the radiometric characteristics,cross-compared in Table III, where the distance to coast, beamwidth, footprint size and beam efficiencies have very similarvalues for all models, while the cross-polarization powers area bit pessimistic for Simplified models I and II. More closeinvestigation of the latter effects indicates the sensitivity ofthe presently used optimum beamforming approach to thevariations and assymetries of the cross-polarization patterns.This will be studied in our future work.

V. CONCLUSIONS

The simplified modeling approach – assuming identical em-bedded element patterns of the phased array feed illuminatinga large reflector – has been validated for the case of a conicalscan radiometer antenna fed with a strongly coupled Vivaldiantenna element array. It has been shown that rather sig-nificant differences between the embedded element patterns,introduced by the edge truncation effects, have relatively weakcontribution to the total compound beam of the array, whenall elements are excited to provide optimum illumination. Asthe result, radiometer characteristics derived from the antennafar-field pattern, such as the beam efficiency, footprint, anddistance to coast can be predicted almost as equally well aswith the full-wave array model – that is important for theantenna system optimization and array prototype developmentphase. When applying this approach to applications withstringent requirements on the cross-poalrization, one couldexpect pessimistic estimation of its levels and the sensitivityto the optimum element excitation choice.

ACKNOWLEDGMENT

The present work has been funded by the Swedish NationalSpace Board. The radiometer requirements have been derivedby the team consisting of TICRA and DTU-Space (Denmark).

REFERENCES

[1] C. Bencivenni, M. Ivashina, R. Maaskant, and J. Wettergren, “Synthesisof maximally sparse arrays using compressive-sensing and full-waveanalysis for global earth coverage,” IEEE Trans. Antennas Propag.,vol. PP, no. 99, pp. 1–6, 2016.

[2] L. Poli, P. Rocca, G. Gottardi, and A. Massa, “Design of simplifiedlarge array structures for preliminary experimental validation,” in 10thEuropean Conference on Antennas and Propagation (EuCAP), Davos,Switzerland, Apr. 2016, pp. 1–4.

[3] (2015) Earth Explorer Mission EE-9. [Online]. Available:http://explorercall.esa.int/index.php/15-mission-ee9

[4] F. Collard et al., “Sea surface temperature, wind and salinity (TWIST),”proposal for the Earth Explorer Mission EE-9, Unpublished.

[5] N. Skou and D. L. Vine, Microwave Radiometer Systems: Design &Analysis. Artech House, 2006.

[6] C. Cappellin, K. Pontoppidan, P. Nielsen, N. Skou, S. S. Søbjærg,A. Ihle, D. Hartmann, M. Ivashina, O.Iupikov, and K. v. t Klooster,“Novel multi-beam radiometers for accurate ocean surveillance,” inProc. European Conference on Antennas and Propag. (EuCAP), TheHague, The Netherlands, Apr. 2014, pp. 1–4.

[7] O. A. Iupikov, M. V. Ivashina, C. Cappellin, and N. Skou, “Digital-beamforming array antenna technologies for future ocean-observingsatellite missions,” in Proc. IEEE AP-S International Symposium, Fa-jardo PR, Jul. 2016, pp. 1–2.

[8] O. A. Iupikov, M. V. Ivashina, K. Pontoppidan, P. H. Nielsen, C. Cap-pellin, N. Skou, S. S. Søbjærg, A. Ihle, D. Hartmann, and K. v. tKlooster, “Dense focal plane arrays for pushbroom satellite radiometers,”in Proc. European Conference on Antennas and Propag. (EuCAP),Hague, The Netherlands, Apr. 2014, pp. 1–5.

[9] C. Cappellin, K. Pontoppidan, P. H. Nielsen, N. Skou, S. S. Søbjærg,A. Ihle, M. V. Ivashina, O. A. Iupikov, and K. v. ’t Klooster, “Design ofa push-broom multi-beam radiometer for future ocean observations,” inProc. European Conference on Antennas and Propag. (EuCAP), Lisbon,Portugal, Apr. 2015, pp. 1–5.

[10] G. W. Kant, P. D. Patel, S. J. Wijnholds, M. Ruiter, and E. van der Wal,“EMBRACE: A multi-beam 20,000-element radio astronomical phasedarray antenna demonstrator,” IEEE Trans. Antennas Propag., vol. 59,no. 6, pp. 1990–2003, Jun. 2011.

[11] O. A. Iupikov, M. V. Ivashina, K. Pontoppidan, P. H. Nielsen, C. Cap-pellin, N. Skou, S. S. Søbjærg, A. Ihle, D. Hartmann, and K. v. tKlooster, “An optimal beamforming algorithm for phased-array antennasused in multi-beam spaceborne radiometers,” in Proc. European Confer-ence on Antennas and Propag. (EuCAP), Lisbon, Portugal, Apr. 2015,pp. 1–5.

[12] M. V. Ivashina, R. Maaskant, and B. Woestenburg, “Equivalent systemrepresentation to model the beam sensitivity of receiving antenna arrays,”IEEE Antennas Wireless Propag. Lett., vol. 7, no. 1, pp. 733–737, Jan.2008.